Bulletin of Volcanology

, Volume 73, Issue 1, pp 39–54 | Cite as

Bubble growth in visco-elastic magma: implications to magma fragmentation and bubble nucleation

  • Kurzon Ittai
  • Lyakhovsky Vladimir
  • Navon Oded
Research Article


We present a visco-elastic bubble growth model, accounting for viscous and elastic deformations and for volatile mass transfer between bubbles and melt. We define the borders between previous bubble growth models accounting for incompressible viscous melt, and our new model accounting also for elastic deformation; this is done by a set of end-member analytical solutions and numerical simulations. Elastic deformation is most prominent for magma of small vesicularity, where the growth regime depends on the shear modulus. For high shear modulus, bubble growth is slow and follows an exponential law in a viscous growth regime, while for low shear modulus bubbles quickly follow a square-root diffusive solution. Our model provides all the elastic components (stresses, strains and strain rates) required for defining criteria for failure and magma fragmentation. We suggest two failure criteria, a stress related one based on the internal friction and the Mohr-Coulomb failure theory, and a strain related one based on fibre elongation experiments. We argue that both criteria are equivalent if we consider their shear modulus dependency and its effect on magma rheology. Last, we apply our model to the process of bubble nucleation. In the incompressible case, following nucleation, growth is slow and leads to long incubation times during which bubbles may be dissolved back into the melt. The elastic response in magmas with low shear modulus results in a short incubation time, increasing the probability of survival. The above effects emphasize the significance of visco-elasticity for the dynamic processes occurring in magmas during volcanic activity.


Relaxation time Visco-elasticity Bubble growth Bubble nucleation Magma fragmentation 



We are indebted to Nadav Lensky for useful discussions. We thank Michael Manga and two anonymous reviewers and the editor, Donald Dingwell, for their constructive reviews and comments, making a great effort to improve the manuscript. Funding was provided by the Israel Science Foundation (grant 324/07).

Supplementary material

445_2010_402_MOESM1_ESM.pdf (72 kb)
Online Resource 1 The analytical elastic end-member solutions (PDF 71 kb)
445_2010_402_MOESM2_ESM.pdf (398 kb)
Online Resource 2 The diffusive bubble growth regime (PDF 398 kb)
445_2010_402_MOESM3_ESM.pdf (173 kb)
Online Resource 3 The model sensitivity to τ k (PDF 172 kb)
445_2010_402_MOESM4_ESM.pdf (49 kb)
Online Resource 4 The condition for applying steady-state failure criteria (PDF 48 kb)


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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Kurzon Ittai
    • 1
    • 2
  • Lyakhovsky Vladimir
    • 2
  • Navon Oded
    • 1
  1. 1.The Fredy and Nadine Herrmann Institute of Earth SciencesThe Hebrew UniversityJerusalemIsrael
  2. 2.The Geological Survey of IsraelJerusalemIsrael

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